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Investigation of the smoking model is important as it has a direct effect on human health. This paper focuses on the numerical analysis of the fractional order giving up smoking model. Nonetheless, due to observational or experimental errors, or any other circumstance, it may contain some incomplete information. Fuzzy sets can be used to deal with uncertainty. Yet, there may be some inconsistency in the membership as well. As a result, the primary goal of this proposed work is to numerically solve the model in a type-2 fuzzy environment.

Triangular perfect quasi type-2 fuzzy numbers (TPQT2FNs) are used to deal with the uncertainty in the model. In this work, concepts of r2-cut at r1-plane are used to model the problem's uncertain parameter. The Legendre wavelet method (LWM) is then utilised to solve the giving up smoking model in a type-2 fuzzy environment.

LWM has been effectively employed in conjunction with the r2-cut at r1-plane notion of type-2 fuzzy sets to solve the model. The LWM has the advantage of converting the non-linear fractional order model into a set of non-linear algebraic equations. LWM scheme solutions are found to be well agreed with RK4 scheme solutions. The existence and uniqueness of the model's solution have also been demonstrated.

To deal with the uncertainty, type-2 fuzzy numbers are used. The use of LWM in a type-2 fuzzy uncertain environment to achieve the model's required solutions is quite fascinating, and this is the key focus of this work.

The fractional order HIV model has an important role in biological science. To study the HIV model in a better way, the model is presented with the help of Atangana- Baleanu operator which is in Caputo sense. Also, the characteristics of the solutions are described briefly with the help of the advance numerical techniques for the different values of fractional order derivatives. This paper aims to discuss the aforementioned objectives.

In this work, Adams-Bashforth method and Euler method are used to get the solution of the HIV model. These are the important numerical methods. The comparison results also are described with the physical meaning of the solutions of the model.

HIV model is analyzed under the view of fractional and AB derivative in Atangana-Baleanu-Caputo sense. The uniqueness of the solution is proved by using Banach Fixed point. The solution is derived with the help of Sumudu transform. Further, the authors employed fractional Adam-Bashforth method and Euler method to enumerate numerical results. The authors have used several values of fractional orders to present the outcomes graphically. The above calculations have been done with the help of MATLAB (R2016a). The numerical scheme used in the proposed study is valid and fruitful, and the same can be used to explore other real issues.

This investigation can be done for the real data sets.

This paper aims to express the solution of the HIV model in a better way with the effect of non-locality, this work is very useful.

In this work, HIV model is developed with the help of Atangana- Baleanu operator in Caputo sense. By using Banach Fixed point, the authors proved that the solution is unique. Also, the solution is presented with the help of Sumudu transform. The behaviors of the solutions are checked for different values of fractional order derivatives with the physical meaning with help of the Adam-Bashforth method and the Euler method.

In this paper, the author presents a hybrid method along with its error analysis to solve (1+2)-dimensional non-linear time-space fractional partial differential equations (FPDEs).

The proposed method is a combination of Sumudu transform and a semi-analytc technique Daftardar-Gejji and Jafari method (DGJM).

The author solves various non-trivial examples using the proposed method. Moreover, the author obtained the solutions either in exact form or in a series that converges to a closed-form solution. The proposed method is a very good tool to solve this type of equations.

The present work is original. To the best of the author's knowledge, this work is not done by anyone in the literature.

The purpose of this paper is to find approximate solutions for a general class of fractional order boundary value problems that arise in engineering applications.

A newly developed semi-analytical scheme will be applied to find approximate solutions for fractional order boundary value problems. The technique is regarded as an extension of the well-established variation iteration method, which was originally proposed for initial value problems, to cover a class of boundary value problems.

It has been demonstrated that the method yields approximations that are extremely accurate and have uniform distributions of error throughout their domain. The numerical examples confirm the method’s validity and relatively fast convergence.

The generalized variational iteration method that is presented in this study is a novel strategy that can handle fractional boundary value problem more effectively than the classical variational iteration method, which was designed for initial value problems.

The purpose of this paper is to study large deviations for the solution processes of a stochastic equation incorporated with the effects of nonlocal condition.

A weak convergence approach is adopted to establish the Laplace principle, which is same as the large deviation principle in a Polish space. The sufficient condition for any family of solutions to satisfy the Laplace principle formulated by Budhiraja and Dupuis is used in this work.

Freidlin–Wentzell type large deviation principle holds good for the solution processes of the stochastic functional integral equation with nonlocal condition.

The asymptotic exponential decay rate of the solution processes of the considered equation towards its deterministic counterpart can be estimated using the established results.

The purpose of this paper is to propose a novel nonlocal fractal calculus scheme dedicated to the analysis of fractal electrical circuit, namely, the generalized nonlocal fractal calculus.

For being generalized, an arbitrary kernel function has been adopted. The condition on order has been derived so that it is not related to the γ-dimension of the fractal set. The fractal Laplace transforms of our operators have been derived.

Unlike the traditional power law kernel-based nonlocal fractal calculus operators, ours are generalized, consistent with the local fractal derivative and use higher degree of freedom. As intended, the proposed nonlocal fractal calculus is applicable to any kind of fractal electrical circuit. Thus, it has been found to be a more efficient tool for the fractal electrical circuit analysis than any previous fractal set dedicated calculus scheme.

A fractal calculus scheme that is more efficient for the fractal electrical circuit analysis than any previous ones has been proposed in this work.

Cities are host to many of the world’s knowledge intensive research and innovation clusters. As such, they are likely to be attractive locations for emerging market multinational enterprises (MNEs) seeking to engage in knowledge seeking “springboard” type firm-level catch-up strategies. The purpose of this study is to therefore explore whether city-based research-intensive clusters containing deep pools of location bounded (i.e. “sticky”) knowledge are a stronger driver for greenfield research and development (R&D)-related FDI projects for Chinese MNEs than they are for developed market MNEs.

The authors use logistic modelling on 97,163 worldwide greenfield FDI projects to explore the relative likelihoods of Chinese MNEs engaging in R&D-related greenfield (i.e. “strategic asset seeking”) FDI projects as well as how city type (global or research-intensive cluster city) moderates this relationship for Chinese MNEs.

The authors find that Chinese MNEs are more likely to engage in overseas R&D FDI projects (compared with other types of project) than DMNEs and that research-intensive city clusters hold a stronger attraction for Chinese MNEs than developed market MNEs.

The authors discuss how the research contributes to the debate on emerging market MNE catch-up theory, as well as that on sub-national city location choice, by highlighting the growing importance of sub-national geography to understanding strategic asset seeking related greenfield FDI.

Sub-national city location choice is an important driver of strategic asset seeking FDI for Chinese MNEs, one that both national and local city level policymakers should pay attention to.

Chinese FDI via aggressive mergers and acquisitions to acquire key technologies has been restricted in recent years. Policymakers must consider whether they may also wish to restrict Chinese greenfield FDI in R&D-related projects, which now exhibit a pronounced upward trend.

The authors highlight the growing importance of sub-national geography to understanding strategic asset seeking related greenfield FDI in Chinese MNEs (and how it plays, more generally, a central role in their strategies).

This study aims to analyse the behaviour of plane waves within a nonlocal transversely isotropic visco-thermoelastic medium having variable thermal conductivity.

The concept of enunciation is used in the generalized theory of thermoelasticity in accordance with the Green–Lindsay and Eringen’s nonlocal elasticity models. The linear viscoelasticity model developed by Kelvin–Voigt is used to characterize the viscoelastic properties of transversely isotropic materials.

It has been noticed that three plane waves, which are coupled together, travel through the medium at three different speeds. The derivation of reflection coefficients and energy ratios for reflected waves is carried out by incorporating suitable boundary conditions. Numerical computations are performed for the amplitude ratios, phase speeds and energy partition and displayed in graphical form.

The outcomes of the numerical simulation demonstrate that the amplitude ratios are significantly influenced by variable thermal conductivity, nonlocal parameters and viscosity. It is further observed from the plots that the phase speeds in a transversely isotropic medium depend on the angle of incidence. In addition, it has been established that the energy is preserved during the reflection phenomenon.

The objective of the proposed work is to identify the most commonly occurring non–small cell carcinoma types, such as adenocarcinoma and squamous cell carcinoma, within the human population. Another objective of the work is to reduce the false positive rate during the classification.

In this work, a hybrid method using convolutional neural networks (CNNs), extreme gradient boosting (XGBoost) and long-short-term memory networks (LSTMs) has been proposed to distinguish between lung adenocarcinoma and squamous cell carcinoma. To extract features from non–small cell lung carcinoma images, a three-layer convolution and three-layer max-pooling-based CNN is used. A few important features have been selected from the extracted features using the XGBoost algorithm as the optimal feature. Finally, LSTM has been used for the classification of carcinoma types. The accuracy of the proposed method is 99.57 per cent, and the false positive rate is 0.427 per cent.

The proposed CNN–XGBoost–LSTM hybrid method has significantly improved the results in distinguishing between adenocarcinoma and squamous cell carcinoma. The importance of the method can be outlined as follows: It has a very low false positive rate of 0.427 per cent. It has very high accuracy, i.e. 99.57 per cent. CNN-based features are providing accurate results in classifying lung carcinoma. It has the potential to serve as an assisting aid for doctors.

It can be used by doctors as a secondary tool for the analysis of non–small cell lung cancers.

It can help rural doctors by sending the patients to specialized doctors for more analysis of lung cancer.

In this work, a hybrid method using CNN, XGBoost and LSTM has been proposed to distinguish between lung adenocarcinoma and squamous cell carcinoma. A three-layer convolution and three-layer max-pooling-based CNN is used to extract features from the non–small cell lung carcinoma images. A few important features have been selected from the extracted features using the XGBoost algorithm as the optimal feature. Finally, LSTM has been used for the classification of carcinoma types.